2003/05/07 by Radu Pantilie, R. Pantilie, J. C. Wood +3
Mathematics · #53C43 #58E20 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG #msc:53C43 #msc:58E20
paper · pdf · doi:10.48550/arxiv.math/0305110
39 pages, LaTeX 2e, using fancyheadings sty. Some minor improvements made. To appear in Q. J. Math
openalex publication_date 2003/05/07 · arxiv created 2005/04/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a general notion of twistorial map and classify twistorial harmonic morphisms with one-dimensional fibres from self-dual four-manifolds. Such maps can be characterised as those which pull back Abelian monopoles to self-dual connections. In fact, the constructions involve solving a generalised monopole equation, and also the Beltrami fields equation of hydrodynamics, and lead to constructions of self-dual metrics.